Economics for CED

Economics for CED

Problem Set #5

1. This question is from Prof. Michelle White’s Law and Economics 118 class, Study Questions for Week 1, question #1 (see http://econ.ucsd.edu/~miwhite/econ118/).

Consider the following gamble. If a six-sided die comes up with a one, then I get

$60. Otherwise I get zero.

(a) What is the expected value of this gamble?

(b) How much would the gamble need to cost to make it fair?

(c) Give the expected utility function of someone playing this gamble.

(d) What type of people would play this gamble at a cost of $10? What if the cost were $8 rather than $10?

2. This question is from Prof. Michelle White’s Law and Economics 118 class, Study Questions for Week 1, question #4 (see http://econ.ucsd.edu/~miwhite/econ118/).

A firm can choose between two projects:

Project A costs 50,000 and has the following payoffs and probabilities

Payoff / 100000 / 0 / 500000 / 1000000
Probability / .5 / .1 / .25 / .15

Project B costs 75,000 and has the following payoffs and probabilities

Payoff / 120000 / 10000 / 0 / 1000000
Probability / .4 / .1 / .2 / .3

Which project should the firm undertake? Assume that the firm wants to choose the project with the highest expected value.

3. This question is from Prof. Michelle White’s Law and Economics 118 class, Lecture #2, page 19 (see http://econ.ucsd.edu/~miwhite/econ118/). See Noémi’s Lecture 5, slides 26-30 on “fair insurance” and maximum premiums for the original example that these questions ask about.

a. Assume that the person has the utility function U=W^(.8). Compared to U= √W = W^(.5), this person is less risk averse. Show that this person’s maximum willingness-to-pay for insurance, m, is less than $58.15.

b. Assume that the person has the utility function U = W = W^1. Show that the maximum willingness-to-pay for insurance m equals the fair insurance premium, f. (U = W is a risk neutral utility function.)

4. This question is from Prof. Michelle White’s Law and Economics 118 class, Study Questions for Week 1, question #8 (see http://econ.ucsd.edu/~miwhite/econ118/).

Steve has wealth of W=$2000. He faces a risk that he might either receive $1000 or be forced to pay $1000, each with .5 probability.

a. What is Steve’s expected utility function?

b. What is the expected value of Steve’s wealth?

c. Suppose Steve’s utility of wealth is U= √W. Also suppose someone offers to insure the uncertainty that Steve faces in return for an insurance premium of P. Find the maximum P that Steve is willing to pay for the insurance. How does this compare to the “fair” insurance premium?

5. This question is from Prof. Michelle White’s Law and Economics 118 class, Study Questions for Week 1, question #10 (see http://econ.ucsd.edu/~miwhite/econ118/).

Give some examples of moral hazard and adverse selection.